A mathematical model for the transmission dynamics of HIV/AIDS in a two-sex population Counseling and Antiretroviral Therapy (ART)

Abstract

An extended version of a one-sex mathematical model of HIV/AIDS transmission dynamics considering Counseling and Antiretroviral Therapy (ART) has been carried out. We proved that the disease-free equilibrium states (DFES) of  the sub-model without ART and the sub-models with only infected males or females receiving ART are locally and asymptotically stable under prescribed conditions on the given model parameters. Threshold conditions are therefore derived, in terms of the given model parameters, for stability of DFES of the sub-models, as well as the proportion of infected people to receive ART. This means that HIV/AIDS can be eradicated under such conditions. Furthermore, results from the numerical experiments show the interplay of the model parameters in the control or eradication of HIV/AIDS. From these results, we see that the control or eradication of HIV/AIDS in heterosexual populations is dependent on the net transmission rates of the infection, the effectiveness of counseling and ART, and proportion of infected people receiving ART for each sex.